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                                                                    Exhibit 32.1

                           CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                 SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

   The undersigned, Eleanor L. Thomas, President (chief executive officer) of
the managing owner, Prudential Securities Futures Management Inc. (the 'Managing
Owner'), of World Monitor Trust II--Series D ('Series D'), hereby certifies,
pursuant to 18 U.S.C. 1350, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that:

   (1) Series D's Quarterly Report on Form 10-Q for the period ending September
       26, 2003, as filed with the Securities and Exchange Commission on the
       date hereof (the 'Quarterly Report'), fully complies with the
       requirements of Section 13(a) or 15(d) of the Securities Exchange Act of
       1934; and

   (2) The information contained in the Quarterly Report fairly presents, in all
       material respects, the financial condition and results of operations of
       Series D.

/s/ Eleanor L. Thomas
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Eleanor L. Thomas
President (chief executive officer) of the Managing Owner
November 10, 2003